Amsterdamse Bos is a vast tract of lakes, woods and meadows criss-crossed by paths. It's filled with activities and is especially great for children. You can rent bicycles, visit the goat farm, kayak the waterways, see a play at the open-air theatre, ascend to the treetops in the climbing park or hang out at the cafes and pancake restaurants.
In the densest thickets you can forget you're near a city at all (though, actually, you're right by Schiphol airport). The forest comprises roughly 1000 hectares of green space. A lot of locals use the park, but it rarely feels crowded.
Take bus 170 or 172 from Centraal Station; the trip takes about 40 minutes.